Conic quadratic modeling

[İrem BAHTİYAR]

Hello I am trying to model the constraint in the screenshot, epsilon and gamma_i s are variables and theta=0.5. I tried to use mf.Domain.inRotatedQCone() this but it seems like it doesnt work. Do you have any idea how can I model this? I am using python.

Thanks.

[Erling D. Andersen]

Is your problem convex?  

Erling D. Andersen

MOSEK APS 

Fruebjergvej 3, 

Symbion Science Park Box 16, 

DK-2100 Copenhagen O

Ph: +45 7174 9373

Mo: +45 2362 9520

fre. 1. aug. 2025, 06.30 skrev İrem BAHTİYAR <irem.ba...@gmail.com>:

Hello I am trying to model the constraint in the screenshot, epsilon and gamma_i s are variables and theta=0.5. I tried to use mf.Domain.inRotatedQCone() this but it seems like it doesnt work. Do you have any idea how can I model this? I am using python.

Thanks.

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[İrem BAHTİYAR]

The mathematical model i am trying to code is below for theta=0.5, a, x and B_i are vectors like a=[-1,0], x=[t,1], and B is a parameter vector.  I think it is convex.

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[Erling D. Andersen]

My thinking is that your model is nonconvex.

Please show us the proof for the claimed convexity. That should be very useful to convert the model to conic form.

[Michal Adamaszek]

When theta=0.5 then the exponent equals theta/(theta-1)=-1. The only nonlinearities in the model are of the form

xi * (gamma/xi)^(-1) = xi^2 / gamma

which is known in most modeling tools as quad_over_lin and the constraint

something >=  xi^2/gamma

is equivalent to

something * gamma >= xi^2

and can be written using the rotated quadratic cone (assuming/enforcing gamma>0). So the model should be possible.

(I am assuming all coefficients like p_i are nonnnegative and the assummed gamma_i is nonnegative etc. as enforced by the remaining convexity requirements of the problem and by the definition of the RSOC cone).

From the statement "I tried to use mf.Domain.inRotatedQCone() this but it seems like it doesnt work" it is not clear what you did, what went wrong, or how to help.

Michal

[Erling D. Andersen]

As far I can see the t in objective appears nowhere in the constraints. 

I misread the 1 in the exponent as t. 

Erling D. Andersen

MOSEK APS 

Fruebjergvej 3, 

Symbion Science Park Box 16, 

DK-2100 Copenhagen O

Ph: +45 7174 9373

Mo: +45 2362 9520

To view this discussion visit https://groups.google.com/d/msgid/mosek/474a0685-9bce-452a-a027-ca3aa0d1e628n%40googlegroups.com.

[İrem BAHTİYAR]

Hello,

Thank you all for your comments. first of all, x is a vector containing t, so there is t in the constraints. I tried exactly what Micheal said and now it is working, thank you again for your help.

Best